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            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/tancik/fourier-feature-networks/blob/master/Experiments/toy_stationary_ex.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3x8yQ-atx8CM",
        "colab_type": "text"
      },
      "source": [
        "#Demonstration of stationary property"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OfWO2IoBx4O6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import jax\n",
        "from jax import random, grad, jit, vmap\n",
        "from jax.config import config\n",
        "import jax.numpy as np\n",
        "from jax.experimental import optimizers, stax\n",
        "\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.pylab as pylab\n",
        "import os\n",
        "\n",
        "from tqdm.notebook import tqdm as tqdm\n",
        "\n",
        "## Random seed\n",
        "rand_key = random.PRNGKey(10)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZXJY2loQyPoK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "d24bde5e-bf73-4804-daa6-1a52caeeb491"
      },
      "source": [
        "signal_length = 256\n",
        "x_min = -np.pi\n",
        "x_max = np.pi\n",
        "x_vals = np.linspace(x_min,x_max,signal_length)[...,None]\n",
        "x_vals_encoded = np.concatenate([np.sin(x_vals), np.cos(x_vals)], axis=-1)\n",
        "\n",
        "def gen_y_vals(x_vals, center, width):\n",
        "    return(np.roll(np.exp(-.5 * ((x_vals)/width)**2), int((center/(2*np.pi))*x_vals.shape[0])))\n",
        "for center in np.linspace(x_min, x_max, 8):\n",
        "    plt.plot(x_vals, gen_y_vals(x_vals, center, .2))\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T0jFFcslzlFx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def make_network(num_layers, num_channels):\n",
        "  layers = []\n",
        "  for i in range(num_layers-1):\n",
        "      layers.append(stax.Dense(num_channels))\n",
        "      layers.append(stax.Relu)\n",
        "  layers.append(stax.Dense(1))\n",
        "  return stax.serial(*layers)\n",
        "\n",
        "init_fn, apply_fn = make_network(4, 256)\n",
        "\n",
        "model_loss = jit(lambda params, x, y: np.mean((apply_fn(params, x) - y) ** 2))\n",
        "model_grad_loss = jit(lambda params, x, y: jax.grad(model_loss)(params, x, y))\n",
        "\n",
        "def train_model(key, lr, iters, data):\n",
        "    opt_init, opt_update, get_params = optimizers.adam(lr)\n",
        "    opt_update = jit(opt_update)\n",
        "\n",
        "    _, params = init_fn(key, (-1, data[0].shape[-1]))\n",
        "    opt_state = opt_init(params)\n",
        "\n",
        "    losses = []\n",
        "    for i in tqdm(range(iters), desc='train iter', leave=False):\n",
        "        opt_state = opt_update(i, model_grad_loss(get_params(opt_state), *data), opt_state)\n",
        "        if i % 50 == 0:\n",
        "            loss = model_loss(get_params(opt_state), *data)\n",
        "            losses.append(loss)\n",
        "    return losses"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LOeBrV2ABITb",
        "colab_type": "text"
      },
      "source": [
        "# Ensemble"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IQX8x1tl2Efo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 17,
          "referenced_widgets": [
            "14220ed103e94c5f99c78807b31e7edc",
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          ]
        },
        "outputId": "12bece3f-0517-4a5b-c7d2-ec0480a1c91d"
      },
      "source": [
        "ensemble_size = 20\n",
        "rand_key = random.PRNGKey(10)\n",
        "ensemble_key = random.split(rand_key, ensemble_size)\n",
        "lr = 1e-4\n",
        "iters = 500\n",
        "no_encoding_losses = []\n",
        "encoded_losses = []\n",
        "centers = np.linspace(x_min, x_max, 40)\n",
        "for center in tqdm(centers, leave=False):\n",
        "    y_vals = gen_y_vals(x_vals, center, .05)\n",
        "    no_encoding_losses.append(vmap(train_model, in_axes=[0,None,None,None])(ensemble_key, lr, iters, (x_vals, y_vals))[-1])\n",
        "    encoded_losses.append(vmap(train_model, in_axes=[0,None,None,None])(ensemble_key, lr, iters, (x_vals_encoded, y_vals))[-1])\n",
        "\n",
        "no_encoding_losses = np.array(no_encoding_losses)\n",
        "encoded_losses = np.array(encoded_losses)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "14220ed103e94c5f99c78807b31e7edc",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=40.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
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            "\r"
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    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MvOkzakY7OfQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "outputId": "04bda6cb-ad58-443c-c133-b67a7e241425"
      },
      "source": [
        "prop_cycle = plt.rcParams['axes.prop_cycle']\n",
        "colors = prop_cycle.by_key()['color']\n",
        "\n",
        "params = {'legend.fontsize': 20,\n",
        "         'axes.labelsize': 18,\n",
        "         'axes.titlesize': 22,\n",
        "         'xtick.labelsize':16,\n",
        "         'ytick.labelsize':16}\n",
        "pylab.rcParams.update(params)\n",
        "\n",
        "\n",
        "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n",
        "matplotlib.rcParams['mathtext.rm'] = 'serif'\n",
        "\n",
        "plt.rcParams[\"font.family\"] = \"cmr10\"\n",
        "\n",
        "\n",
        "colors_k = np.array([[0.8872, 0.4281, 0.1875],\n",
        "    # [0.8136, 0.6844, 0.0696],\n",
        "    [0.2634, 0.6634, 0.4134],\n",
        "    [0.0943, 0.5937, 0.8793],\n",
        "    [0.3936, 0.2946, 0.6330],\n",
        "    [0.7123, 0.2705, 0.3795]])\n",
        "\n",
        "fig = plt.figure(constrained_layout=True, figsize=(14,4))\n",
        "gs = fig.add_gridspec(1,2)\n",
        "\n",
        "centers_to_highlight = [-np.pi/2,0,np.pi/2]\n",
        "linewidth = 4\n",
        "title_offset = -.35\n",
        "\n",
        "ax = fig.add_subplot(gs[0,0])\n",
        "for i, center in enumerate(centers_to_highlight):\n",
        "    plt.plot(x_vals, gen_y_vals(x_vals, center, .05), linewidth=linewidth, color=colors_k[i], alpha=.8)\n",
        "plt.xlabel('$x$')\n",
        "plt.ylabel('$y$')\n",
        "plt.yticks([0,.25,.5,.75,1], ['$0$','','','','$1$'])\n",
        "plt.grid(True, which='major', alpha=.3)\n",
        "ax.set_title('(a) Example target signals', y=title_offset)\n",
        "\n",
        "plt.xticks([-np.pi, -np.pi/2, 0, np.pi/2, np.pi], ['$-\\pi$','$-\\pi/2$','$0$','$\\pi/2$','$\\pi$'])\n",
        "\n",
        "ax = fig.add_subplot(gs[0,1])\n",
        "for i, center in enumerate(centers_to_highlight):\n",
        "    ax.vlines(center, ymin=0, ymax=70, color=colors_k[i], linestyle=':', linewidth=linewidth, alpha=.8)\n",
        "\n",
        "\n",
        "no_encoding_mean = np.mean(no_encoding_losses, axis=-1)\n",
        "no_encoding_std = np.std(no_encoding_losses, axis=-1)\n",
        "plt.semilogy(centers, no_encoding_mean, color=colors_k[-1], linewidth=linewidth, label='No Mapping')\n",
        "plt.fill_between(centers, no_encoding_mean-no_encoding_std, no_encoding_mean+no_encoding_std, color=colors_k[-1], alpha=.15)\n",
        "\n",
        "encoded_mean = np.mean(encoded_losses, axis=-1)\n",
        "encoded_std = np.std(encoded_losses, axis=-1)\n",
        "plt.semilogy(centers, encoded_mean, color=colors_k[-2], linewidth=linewidth, label='Basic Mapping')\n",
        "plt.fill_between(centers, encoded_mean-encoded_std, encoded_mean+encoded_std, color=colors_k[-2], alpha=.15)\n",
        "plt.xlabel('Center of Gaussian')\n",
        "plt.ylabel('Mean squared error')\n",
        "plt.ylim([.0001,.02])\n",
        "plt.grid(True, which='major', alpha=.3)\n",
        "\n",
        "plt.xticks([-np.pi, -np.pi/2, 0, np.pi/2, np.pi], ['$-\\pi$','$-\\pi/2$','$0$','$\\pi/2$','$\\pi$'])\n",
        "\n",
        "ax.set_title('(b) Reconstruction accuracy', y=title_offset)\n",
        "plt.legend(loc='center left', bbox_to_anchor=(1,.5), handlelength=1)\n",
        "\n",
        "plt.savefig('supp_stationary.pdf', bbox_inches='tight', pad_inches=0)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1008x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fvuhliF-CLEz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}